Annual Interest versus Monthly Interest?

Paul_Herring

@Paul Herring
Can you provide a few words that summarise and illustrate the fundamental underlying mathematics illustrated in your table. A conclusion would also be of use. References for the equations would complete the study.

I did include a link to the spreadsheet I used

For those interested, but can't be bothered to download said spreadsheet:

1) Yearly interest was a reasonably simple calculation; On month 12:

New Balance = Balance + Round(Balance * (Gross% * (1-Tax%)))

i.e. apply the gross rate, then remove the tax portion and add to the initial balance. The Round() bit removes the fractional pennies

2) Monthly interest is similar:

New Balance = Balance + Round(Balance * ((Gross%/12) * (1-Tax%)))

Only difference being that 1/12th of the interest is applied each month. Again - fractional pennies are removed. On the 2nd month, the 1st month's total is used instead of the initial deposit.

Finally, the net rate is calculated as
(Final Balance - Initial Balance)/Initial Balance.

In a moment of boredom I decided to see what affect the Tax rate has on the difference between monthly net rates and yearly net rates. Seems the worst case is if the tax rate is 55% - either side it drops off to the best case of 0% where (surprisingly) you're better off with monthly:


Tax rate Monthly Yearly Difference
0% 5.002% 5.000% -0.002%
5% 4.746% 4.750% 0.004%
10% 4.491% 4.500% 0.009%
15% 4.237% 4.250% 0.013%
20% 3.983% 4.000% 0.017%
25% 3.728% 3.750% 0.022%
30% 3.477% 3.500% 0.023%
35% 3.226% 3.250% 0.024%
40% 2.975% 3.000% 0.025%
45% 2.724% 2.750% 0.026%
50% 2.473% 2.500% 0.027%
55% 2.222% 2.250% 0.028%
60% 1.974% 2.000% 0.026%
65% 1.725% 1.750% 0.025%
70% 1.477% 1.500% 0.023%
75% 1.229% 1.250% 0.021%
80% 0.984% 1.000% 0.016%
85% 0.733% 0.750% 0.017%
90% 0.492% 0.500% 0.008%
95% 0.240% 0.250% 0.010%
100% 0.000% 0.000% 0.000%


[Edit: Corrected the equations - I'd forgotten to add the old balance to the interest earned!]

Joe_Bloggs

If you wish to view Excel documents you can download the Excel viewer from Microsoft here
J_B.

tomstickland

It doesn't make any difference if you use the AER figure to compare savings accounts.
If you don't then:
- an annual payer pays the gross rate per year, so the net interest will that minus tax.
-a monthly payer pays 1/12th of the gross rate per month and then compounds that 12 times.

masonic

tomstickland wrote:

It doesn't make any difference if you use the AER figure to compare savings accounts.
If you don't then:
- an annual payer pays the gross rate per year, so the net interest will that minus tax.
-a monthly payer pays 1/12th of the gross rate per month and then compounds that 12 times.

Actually, it does matter if you are making regular payments into an account. The AER is calculated assuming a fixed balance. If the balance starts off small, then there is less interest paid initially, so there is less to compound (in the case of monthly interest), so you would earn slightly more from an annual account with the same AER. The converse is true if you reduce your balance over the course of the year.

There is also the fact that tax is deducted on monthly interest as it is paid, and that has a negative impact on compounding for taxpayers.

Oh, and way to bump a 2 year old thread, Tom.

steadynerve

These differences seem fairly small re tax and rising reducing balancses.
I think in practice admin/time over heads make a much bigger difference.

Personally speaking to get the best rates you always have to switch accounts when rates change or better acccounts become availabe.(if higher interest accounts open up you want to move into them-whether interest rates are generally falling or rising) Monthly interest makes this easier as you can just transfer the fuds across by BACS etc - you do not have to worry about closing the account to bring across annual interest payable. This makes monthly my considered choice unless you want to delay your tax payment to another tax year due to allowances etc and are using annula payment dates to do this.

Loughton_Monkey

When banks issue an account in which you have an option for Annual or Monthly, they invariably use the same 'daily rate'.

You do not need to be mathematician to understand the obvious conclusion. In monthly interest, a small part (i.e. tax on the monthly payment) is deducted earlier [and therefore capable of being invested elsewhere] and so leaving the net interest in the account, rolling up, will produce an annual figure less than if you chose Annual Interest.

masonic

steadynerve wrote: »

These differences seem fairly small re tax and rising reducing balancses.
I think in practice admin/time over heads make a much bigger difference.

If you have a choice, it's usually just a case of ticking the appropriate box when applying for the account, or a simple choice between two accounts paying the same rate but with different interest options. There should be no overhead involved since you will have to make a choice whatever you do.

Personally speaking to get the best rates you always have to switch accounts when rates change or better acccounts become availabe.(if higher interest accounts open up you want to move into them-whether interest rates are generally falling or rising) Monthly interest makes this easier as you can just transfer the fuds across by BACS etc - you do not have to worry about closing the account to bring across annual interest payable. This makes monthly my considered choice unless you want to delay your tax payment to another tax year due to allowances etc and are using annula payment dates to do this.

The financial landscape is quite different now compared to how it was back in the olden days of this thread. The best instant access rate (for a couple of years or so) is offered in a current account (if you have £5-21k), and there has been no need to ditch and switch of late because there is no competition to speak of. If you want a good rate generally you have to fix for several years, which almost always means annual interest.

How we'd love to see accounts paying 5% (let alone 5.65%) that we all took for granted in this thread.